Reduce to lowest terms: $ \dfrac{1}{7} \div \dfrac{7}{4} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{7}{4}$ is $ \dfrac{4}{7}$ Therefore: $ \dfrac{1}{7} \div \dfrac{7}{4} = \dfrac{1}{7} \times \dfrac{4}{7} $ $ \phantom{ \dfrac{1}{7} \times \dfrac{4}{7}} = \dfrac{1 \times 4}{7 \times 7} $ $ \phantom{ \dfrac{1}{7} \times \dfrac{4}{7}} = \dfrac{4}{49} $